Finite Group Databasebeta

D4×D61⋊M16 #30625382

order15616
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productD4×D61⋊M16
unambiguous semidirect productD61⋊(D4×M16)

Splittings

SylowC61 ⋊ C2×D4×M16

Subgroups

subgroupG/H
centerC2×C4C23×#6923
commutator, socleC22×C61C24×C4
FrattiniC22C24×#6923
FittingC2×C4×D4×C61C4
prime radicalC22×D4×D61C4
cosocleC2×Dic61C25
hypercenterC2×C4×D4#6923
hypocenterC61C2×D4×M16
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C4×D4

3218 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1114937);